Nicholas Williams

me my email address
I am a JSPS short-term postdoctoral research fellow at the University of Tokyo working with Osamu Iyama.

My research concerns higher-dimensional phenomena in the representation theory of algebras and in combinatorics. I am particularly interested in higher Auslander–Reiten theory, the higher Stasheff–Tamari orders, and the higher Bruhat orders.

You can find a copy of my CV here (updated 22/6/22).

GitHub, ResearchGate, Google Scholar, ORCID iD iconORCID

Preprints

12/2021 Quiver combinatorics for higher-dimensional triangulations, arXiv.
06/2021 The two higher Stasheff–Tamari orders are equal, arXiv.
12/2020 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders, arXiv.

Publications

To appear New interpretations of the higher Stasheff–Tamari orders
Advances in Mathematics. arXiv.
04/2022 Higher-dimensional combinatorics in representation theory
Doctoral thesis, University of Cologne. Link.
09/2021 The combinatorics of tensor products of higher Auslander algebras of type A, (with J. McMahon)
Glasgow Mathematical Journal. DOI, arXiv.

Conference proceedings

To appear The higher Stasheff–Tamari orders in representation theory
Proceedings of the 2020 International Conference on Representations of Algebras.
2021 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Extended abstract published in Proceedings of the 33rd International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire 85B (2021), Art. 6, 12. Link.

Recent talks

6/2022 Mutating cluster-tilting objects in (d + 2)-angulated cluster categories
FD seminar
6/2022 Cyclic polytopes and higher Auslander–Reiten theory I
Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University
4/2022 Equivalence of maximal green sequences
Working seminar in algebra and geometry, University of Cologne
2/2022 Equivalence of maximal green sequences
Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche
1/2022 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Formal Power Series and Algebraic Combinatorics
1/2022 An algebraic interpretation of the higher Stasheff–Tamari orders
Aachen–Bochum–Cologne Darstellungstheorie Seminar
12/2021 Cyclic polytopes and higher Auslander–Reiten theory
Tokyo–Nagoya algebra seminar
6/2021 The higher Stasheff–Tamari orders on triangulations of cyclic polytopes
London Mathematical Society Graduate Student Meeting
5/2021 The two higher Stasheff–Tamari orders are equal
Working seminar in algebra and geometry, University of Cologne
4/2021 The higher Stasheff–Tamari orders in representation theory
Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche
3/2021 New interpretations of the higher Stasheff–Tamari orders
Diskrete Mathematik / Geometrie Forschungsseminar, TU Berlin
3/2021 The Tamari lattice in representation theory
Junior Algebra Colloquium, University of Bristol

Translations

I have translated a couple of papers of Carathéodory from German into English. I make no claim to any of the mathematics in these papers. It is also not impossible that I have introduced errors in the process of translation.

Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen
Constantin Carathéodory
Mathematische Annalen (1907), Volume: 64, pp. 95–115.
Original, Translation
Über den Variabilitätsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen
Constantin Carathéodory
Rendiconti del Circolo Matematico di Palermo (1911), Volume: 32, pp. 193–217.
Original, Translation

Categorifications in Representation Theory

I organised this conference with Aran Tattar.
Conference poster

Other

I am sometimes asked what the painting behind me on zoom is. It is one of my uncle's paintings. You can find more of his paintings here.

Leicester mathematician takes his research to Parliament